%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU407+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:12:12 PM UTC 2026
% Result : Theorem 1.15s 1.63s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 13 unt; 0 def)
% Number of atoms : 198 ( 24 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 240 ( 99 ~; 88 |; 32 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-6 aty)
% Number of variables : 89 ( 2 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(t7_latsum_1,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,u1_struct_0(X1))
| r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_latsum_1) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( l1_orders_2(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(fc2_latsum_1,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( ~ v3_struct_0(k1_latsum_1(X1,X2))
& v1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_latsum_1) ).
fof(d2_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( ( v1_orders_2(X3)
& l1_orders_2(X3) )
=> ( X3 = k1_latsum_1(X1,X2)
<=> ( u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
& u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& l1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,u1_struct_0(X1))
| r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t7_latsum_1])]) ).
fof(c_0_13,plain,
! [X157] :
( v3_struct_0(X157)
| ~ l1_struct_0(X157)
| ~ v1_xboole_0(u1_struct_0(X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_14,plain,
! [X140] :
( ~ l1_orders_2(X140)
| l1_struct_0(X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
fof(c_0_15,plain,
! [X187,X188] :
( ~ m1_subset_1(X187,X188)
| v1_xboole_0(X188)
| r2_hidden(X187,X188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_16,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& l1_orders_2(esk1_0)
& ~ v3_struct_0(esk2_0)
& l1_orders_2(esk2_0)
& m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
& ~ r2_hidden(esk3_0,u1_struct_0(esk1_0))
& ~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( ~ v3_struct_0(k1_latsum_1(X1,X2))
& v1_orders_2(k1_latsum_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc2_latsum_1]) ).
cnf(c_0_18,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( l1_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X158,X159] :
( ( ~ v3_struct_0(k1_latsum_1(X158,X159))
| v3_struct_0(X158)
| ~ l1_orders_2(X158)
| ~ l1_orders_2(X159) )
& ( v1_orders_2(k1_latsum_1(X158,X159))
| v3_struct_0(X158)
| ~ l1_orders_2(X158)
| ~ l1_orders_2(X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_23,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_orders_2(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( v1_xboole_0(u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X116,X117,X118] :
( ( u1_struct_0(X118) = k2_xboole_0(u1_struct_0(X116),u1_struct_0(X117))
| X118 != k1_latsum_1(X116,X117)
| ~ v1_orders_2(X118)
| ~ l1_orders_2(X118)
| ~ l1_orders_2(X117)
| ~ l1_orders_2(X116) )
& ( u1_orders_2(X118) = k2_xboole_0(k2_xboole_0(u1_orders_2(X116),u1_orders_2(X117)),k7_relset_1(u1_struct_0(X116),u1_struct_0(X116),u1_struct_0(X117),u1_struct_0(X117),u1_orders_2(X116),u1_orders_2(X117)))
| X118 != k1_latsum_1(X116,X117)
| ~ v1_orders_2(X118)
| ~ l1_orders_2(X118)
| ~ l1_orders_2(X117)
| ~ l1_orders_2(X116) )
& ( u1_struct_0(X118) != k2_xboole_0(u1_struct_0(X116),u1_struct_0(X117))
| u1_orders_2(X118) != k2_xboole_0(k2_xboole_0(u1_orders_2(X116),u1_orders_2(X117)),k7_relset_1(u1_struct_0(X116),u1_struct_0(X116),u1_struct_0(X117),u1_struct_0(X117),u1_orders_2(X116),u1_orders_2(X117)))
| X118 = k1_latsum_1(X116,X117)
| ~ v1_orders_2(X118)
| ~ l1_orders_2(X118)
| ~ l1_orders_2(X117)
| ~ l1_orders_2(X116) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])]) ).
fof(c_0_26,plain,
! [X130,X131] :
( ( v1_orders_2(k1_latsum_1(X130,X131))
| ~ l1_orders_2(X130)
| ~ l1_orders_2(X131) )
& ( l1_orders_2(k1_latsum_1(X130,X131))
| ~ l1_orders_2(X130)
| ~ l1_orders_2(X131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])]) ).
fof(c_0_27,plain,
! [X119,X120,X121,X122,X123,X124,X125,X126] :
( ( ~ r2_hidden(X122,X121)
| r2_hidden(X122,X119)
| r2_hidden(X122,X120)
| X121 != k2_xboole_0(X119,X120) )
& ( ~ r2_hidden(X123,X119)
| r2_hidden(X123,X121)
| X121 != k2_xboole_0(X119,X120) )
& ( ~ r2_hidden(X123,X120)
| r2_hidden(X123,X121)
| X121 != k2_xboole_0(X119,X120) )
& ( ~ r2_hidden(esk4_3(X124,X125,X126),X124)
| ~ r2_hidden(esk4_3(X124,X125,X126),X126)
| X126 = k2_xboole_0(X124,X125) )
& ( ~ r2_hidden(esk4_3(X124,X125,X126),X125)
| ~ r2_hidden(esk4_3(X124,X125,X126),X126)
| X126 = k2_xboole_0(X124,X125) )
& ( r2_hidden(esk4_3(X124,X125,X126),X126)
| r2_hidden(esk4_3(X124,X125,X126),X124)
| r2_hidden(esk4_3(X124,X125,X126),X125)
| X126 = k2_xboole_0(X124,X125) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
cnf(c_0_28,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v3_struct_0(k1_latsum_1(esk1_0,esk2_0))
| ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
l1_orders_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,plain,
( u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
| X1 != k1_latsum_1(X2,X3)
| ~ v1_orders_2(X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
( l1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( v1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( r2_hidden(X1,X3)
| r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| X2 != k2_xboole_0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_38,plain,
( u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( r2_hidden(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))
| ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(c_0_43,plain,
! [X202,X203] :
( ~ r2_hidden(X202,X203)
| ~ v1_xboole_0(X203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_44,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(esk2_0))
| ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
fof(c_0_45,plain,
! [X189,X190] : k2_xboole_0(X189,k4_xboole_0(X190,X189)) = k2_xboole_0(X189,X190),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_46,plain,
! [X162,X163] :
( v1_xboole_0(X162)
| ~ v1_xboole_0(k2_xboole_0(X163,X162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])]) ).
cnf(c_0_47,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,negated_conjecture,
r2_hidden(esk3_0,u1_struct_0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_30]),c_0_31])]) ).
cnf(c_0_49,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
( v1_xboole_0(X1)
| ~ v1_xboole_0(k2_xboole_0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( v1_xboole_0(k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))
| r2_hidden(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_30]),c_0_31])]) ).
cnf(c_0_52,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
r2_hidden(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU407+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 03:03:16 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 1.15/1.63 % Version : CSE_E---1.7
% 1.15/1.63 % Problem : theBenchmark.p
% 1.15/1.63 % SZS status Theorem for theBenchmark.p
% 1.15/1.63 % SZS output start CNFRefutation
% See solution above
% 1.15/1.63 % Total time : 1.361s
%------------------------------------------------------------------------------